Medium · Probability & Combinatorics · Numerical · ~6 min · #55
A Fair Flip from a Biased Coin
Real interview · Jane Street, Akuna Capital
A coin lands heads with probability . Describe a procedure that uses it to produce an event with probability exactly .
Using the standard pairing procedure (flip twice; HT means "yes", TH means "no", otherwise repeat), what is the expected total number of flips?
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Worked solution
Give the problem an honest attempt first, then reveal the full explanation.
Reported in interviews
- Jane StreetGlassdoor interview question
- Akuna CapitalGlassdoor interview question
Asked with a coin that lands heads 70% of the time.
Candidate-reported and unverified; the firm may phrase it differently or no longer ask it. The wording here is our own paraphrase, and the solution was written and checked independently of any answers posted at the source.
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